Gravity and BF theory defined in bounded regions

Abstract

We study Einstein gravity in a finite spatial region. By requiring a well-defined variational principle, we identify all local boundary conditions, derive surface observables, and compute their algebra. The observables arise as induced surface terms, which contribute to a non-vanishing Hamiltonian. Unlike the asymptotically flat case, we find that there are an infinite number of surface observables. We give a similar analysis for SU(2) BF theory.

References added

References in corpus (1)

• Generalized boundary conditions for general relativity for the asymptotically flat case in terms of Ashtekar's variables

Cited by in corpus (20)

• Edge modes and corner ambiguities in 3d Chern-Simons theory and gravity
• Lorentz-diffeomorphism edge modes in 3d gravity
• Extended actions, dynamics of edge modes, and entanglement entropy
• Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
• Gravitational Statistical Mechanics: A model
• Apparent horizons, black hole entropy and loop quantum gravity
• On a class of 2-surface observables in general relativity
• Abelian BF-Theory and Spherically Symmetric Electromagnetism
• On the Universality of the Entropy-Area Relation
• The thermodynamics of quantum spacetime histories
• Hamiltonian analysis of a topological theory in the presence of boundaries
• Quasilocal Energy for Spin-net Gravity
• Perturbative BF theory
• Canonical analysis of field theories in the presence of boundaries: Maxwell+Pontryagin
• Corners of gravity: the case of gravity as a constrained BF theory
• Point particles in 2+1 dimensions: general relativity and loop gravity descriptions
• The Internal Spin Angular Momentum of an Asymptotically Flat Spacetime
• On energy for accelerating observers in black hole spacetimes
• Weakly Isolated Horizons: $3+1$ decomposition and canonical formulations in self-dual variables
• Condensation of area quanta ensembles with quantum statistics in Schwarzschild spacetimes